





'''simple docstring'''


def 						__a(SCREAMING_SNAKE_CASE_	:       int		,							SCREAMING_SNAKE_CASE_	:       int     ):



    '''simple docstring'''





    _lowerCAmelCase						      =   1  # To kept the Calculated Value
    # Since C(n, k) = C(n, n-k)
    if k > (n - k):
        _lowerCAmelCase						      =   n - k
    # Calculate C(n,k)
    for i in range(SCREAMING_SNAKE_CASE_     ):
        result *= n - i
        result //= i + 1
    return result


def 						__a(SCREAMING_SNAKE_CASE_	:       int     ):



    '''simple docstring'''





    return binomial_coefficient(2 * node_count		,							SCREAMING_SNAKE_CASE_     ) // (node_count + 1)


def 						__a(SCREAMING_SNAKE_CASE_	:       int     ):



    '''simple docstring'''





    if n < 0:
        raise ValueError("factorial() not defined for negative values"     )
    _lowerCAmelCase						      =   1
    for i in range(1		,							n + 1     ):
        result *= i
    return result


def 						__a(SCREAMING_SNAKE_CASE_	:       int     ):



    '''simple docstring'''





    return catalan_number(SCREAMING_SNAKE_CASE_     ) * factorial(SCREAMING_SNAKE_CASE_     )


if __name__ == "__main__":
       _SCREAMING_SNAKE_CASE									=				int(input("Enter the number of nodes: ").strip() or 0)
       if node_count <= 0:
              raise ValueError("We need some nodes to work with.")
       print(
           f'''Given {node_count} nodes, there are {binary_tree_count(node_count)} '''
           f'''binary trees and {catalan_number(node_count)} binary search trees.'''
       )






"""simple docstring"""



from collections import Counter
from timeit import timeit
def      UpperCAmelCase     (       _lowercase :   str = ""			,   )						-> bool:


	"""simple docstring"""




	return sum(c % 2 for c in Counter(input_str.replace(''' '''			,   ''''''	).lower()	).values()	) < 2
def      UpperCAmelCase     (       _lowercase :   str = ""	)						-> bool:


	"""simple docstring"""




	if len(_lowercase	) == 0:
		return True
	lowerCAmelCase_      							=			input_str.replace(''' '''			,   ''''''	).lower()
	# character_freq_dict: Stores the frequency of every character in the input string
	lowerCAmelCase_      							=			{}

	for character in lower_case_input_str:
		lowerCAmelCase_      							=			character_freq_dict.get(_lowercase			,   0	) + 1
	lowerCAmelCase_      							=			0

	for character_count in character_freq_dict.values():
		if character_count % 2:
			odd_char += 1
	if odd_char > 1:
		return False
	return True
def      UpperCAmelCase     (       _lowercase :   str = ""	)						-> None:


	"""simple docstring"""




	print('''\nFor string = '''			,   _lowercase			,   ''':'''	)
	print(
	    '''> can_string_be_rearranged_as_palindrome_counter()'''			,   '''\tans ='''			,   can_string_be_rearranged_as_palindrome_counter(_lowercase	)			,   '''\ttime ='''			,   timeit(
	        '''z.can_string_be_rearranged_as_palindrome_counter(z.check_str)'''			,   setup='''import __main__ as z'''			,   )			,   '''seconds'''			,   )
	print(
	    '''> can_string_be_rearranged_as_palindrome()'''			,   '''\tans ='''			,   can_string_be_rearranged_as_palindrome(_lowercase	)			,   '''\ttime ='''			,   timeit(
	        '''z.can_string_be_rearranged_as_palindrome(z.check_str)'''			,   setup='''import __main__ as z'''			,   )			,   '''seconds'''			,   )


if __name__ == "__main__":
		lowercase_							=							input(
		    'Enter string to determine if it can be rearranged as a palindrome or not: '
		).strip()
		benchmark(check_str)
		lowercase_							=							can_string_be_rearranged_as_palindrome_counter(check_str)
		print(f"""{check_str} can {'' if status else 'not '}be rearranged as a palindrome""")